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| BLACK HOLE THERMODYNAMICS |
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| Black Hole Thermodynamics Although there is no direct empirical input into quantum gravity, physicists hope to accomplish unification by working on the requirement that there must exist a mathematically self consistent theory which accounts for both general relativity and quantum mechanics as they are separately confirmed experimentally. It is important to stress the point that no complete theory satisfying this requirement has yet been found. If just one theory could be constructed then it would have a good chance of being correct. Because of the stringent constraints that self consistency enforces, it is possible to construct thought experiments which provide strong hints about the properties a theory of quantum gravity has to have. There are two physical regimes in which quantum gravity is likely to have significant effects. In the conditions which existed during the first Planck unit of time in our universe, matter was so dense and hot that unification of gravity and other forces would have been realised. Likewise, a small black hole who's mass corresponds to the Planck unit of mass provides a thought laboratory for quantum gravity. Black holes have the property that the surface area of their event horizons must always increase. This is suggestively similar to the law that entropy must increase, and it led Bekenstein to conjecture that the area of the event horizon of a black hole is in fact proportional to its entropy. If this is the case then a black hole would have to have a temperature and obey the laws of thermodynamics. In the 1970's Stephen Hawking investigated the effects of quantum mechanics near a black hole using semi-classical approximations to quantum gravity. He discovered the unexpected result that black holes do emit thermal radiation in a way consistent with the entropy law of Bekenstein. This forces us to conclude that black holes can emit particles and eventually evaporate.For astronomical sized black holes the temperature of the radiation is minuscule and certainly beyond detection, but for small black holes the temperature increases until they explode in one final blast. Hawking realised that this creates a difficult paradox which would surely tell us a great deal about the nature of quantum gravity if we could understand it. The entropy of a system can be related to the amount of information required to describe it. When objects are thrown into a black hole the information they contain is hidden from outside view because no message can return from inside. Now if the blackhole evaporates, this information will be lost in contradiction to the laws of thermodynamics. This is known as the black hole information loss paradox. A number of ways on which this paradox could be resolved have been proposed. The main ones are,The lost information escapes to another universe The final stage of black hole evaporation halts leaving a remnant particle which holds the information. There are strict limits on the amount of information held within any region of space to ensure that the information which enters a black hole cannot exceed the amount represented by its entropy. Something else happens which is so strange we can't bring ourselves to think of it. The first solution would imply a breakdown of quantum coherence. We would have to completely change the laws of quantum mechanics to cope with this situation. The second case is not quite so bad but it does seem to imply that small black holes must have an infinite number of quantum numbers which would mean their rate of production during the big bang would have been divergent. It might be possible to find a way round this but anyway, it is an ugly solution! Assuming that I have not missed something out, which is a big assumption, we must conclude that the amount of entropy which can be held within a region of space is limited by the area of a surface surrounding it. This is certainly counterintuitive because you would imagine that you could write information on bits of paper and the amount you could cram in would be limited by the volume only. This is false because any attempt to do that would eventually cause a black hole to form. Note that this rule does not force us to conclude that the universe must be finite because there is a hidden assumption that the region of space is static which I did not mention. If the amount of information is limited then the number of physical degrees of freedom in a field theory of quantum gravity must also be limited. Inspired by this observation, Gerard 't Hooft, Leonard Susskind and others have proposed that the laws of physics should be described in terms of a discrete field theory defined on a space-time surface rather than throughout space-time. They liken the way this might work to that of a hologram which holds a three dimensional image within its two dimensional surface. Rather than being rejected as a crazy idea, this theory has been recognised by many other physicists as being consistent with other ideas in quantum gravity. |
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